A large tank open to the atmosphere at the to | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The rate of flow of water through a hole is given by the product of the velocity of efflux and the area of the hole.$\frac{\Delta V}{\Delta t} = v

Vedclass · Accepted Answer

$2.5$

Vedclass · Answer

(C) The rate of flow of water through a hole is given by the product of the velocity of efflux and the area of the hole.$\frac{\Delta V}{\Delta t} = v 	imes A$Using Torricelli's law, the velocity of efflux is $v = \sqrt{2gh}$.Thus, $\frac{\Delta V}{\Delta t} = \sqrt{2gh} 	imes A$ ... $(i)$Given:$h = 20 \,m$$g = 10 \,m/s^2$$\frac{\Delta V}{\Delta t} = 3 	imes 10^{-3} \,m^3/min = \frac{3 	imes 10^{-3}}{60} \,m^3/s = 0.5 	imes 10^{-4} \,m^3/s = 5 	imes 10^{-5} \,m^3/s$Substituting the values into equation $(i)$:$5 	imes 10^{-5} = \sqrt{2 	imes 10 	imes 20} 	imes A$$5 	imes 10^{-5} = \sqrt{400} 	imes A$$5 	imes 10^{-5} = 20 	imes A$$A = \frac{5 	imes 10^{-5}}{20} = 0.25 	imes 10^{-5} \,m^2 = 2.5 	imes 10^{-6} \,m^2$Since $1 \,m^2 = 10^6 \,mm^2$, we have:$A = 2.5 	imes 10^{-6} 	imes 10^6 \,mm^2 = 2.5 \,mm^2$.

Similar Questions

$A$ container has a hole of cross-sectional area $1 \, cm^2$ at its bottom. If water is poured into the container at a rate of $70 \, cm^3/s$, what is the maximum height (in $cm$) to which the water can be filled?

$A$ vessel completely filled with water has holes $A$ and $B$ at depths $h$ and $3h$ from the top respectively. The hole $A$ is a square of side $L$ and $B$ is a circle of radius $r$. The water flowing out per second from both the holes is same. Then $L$ is equal to

The water is filled up to a height of $12\, \text{m}$ in a tank having vertical sidewalls. $A$ hole is made in one of the walls at a depth $h$ below the water level. The value of $h$ for which the emerging stream of water strikes the ground at the maximum range is $.....\, \text{m}$.

$A$ large tank filled with water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from $h$ to $h/2$ and from $h/2$ to $0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module